Peculiar graduate in music (5)
I believe the answer is:
rumba
'music' is the definition.
(rumba is a kind of music)
'peculiar graduate' is the wordplay.
'peculiar' becomes 'rum' (synonyms).
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'rum'+'ba'='RUMBA'
'in' acts as a link.
(Other definitions for rumba that I've seen before include "Latin beat" , "Umbra (anag)" , "Lively Cuban dance" , "number of steps" , "music one can dance to" .)